John-Doe - Thanks for the compliment, however, I cannot, in all good conscience, recommend that a hypothyroid patient go the route you are suggesting either. I went to Dr. Fleches for a couple of years - his office is just down the road from me when I am in NC so I tried that approach, and while I know that some people worship him/his way of doing things, I could never recommend it for anyone. Nice guy though (can't say that about some of the other people I had to deal with in his practice though - and there are the criminal charges that are a bit unsettling). The Iodoral however made me much sicker than I have ever been in my life. I just can't go along with extreme measures in just about any area of life.
Steve - Diet is critical. And you may want to learn more about the condition via Mary Shomon's website/forum/books. And, in my experience, keeping the TSH levels between about .02 and .1 (well below the top of the current 'range') is best for many people I know with this problem, and that includes me. For how you 'feel', usually the lower the better but there are potential long term issues with the lowest levels too. The range for diagnosis and maintenance has changed over the years but I am still encountering doctors who think the old scale or even the new scale at the upper ranges is 'normal' and adequate. And it is almost impossible to convince a doctor who is 'old school' about the numbers - move on. If they don't listen to you about how you FEEL and are not willing to try another approach, move on. Perhaps try to seek out a doctor who has the condition him or herself - you may get more understanding there. Or try a homeopath - I had one in TX who diagnosed me within a few minutes when many other doctors totally missed it - they may be open to different approaches to treatment and to the 'how do you feel' thing. This can be an insidious condition, with slow deterioration over time, if you are not optimally treated and treatment varies from one person to another - there is no formula that works for everyone!
This is a battle many of us who are hypothyroid fight (for me it has been well over 20 years now too) - and most of us can tell you it is not an easy road nor a smooth one. We get used to feeling less than we could. We pile on a few pounds here or there and attribute it to getting older - but we can never get them off despite our best efforts. We feel dynamic one day but horrible another if out of balance but accept that we feel sub par but not awful as 'optimum' after years of trying to get back to what we vaguely remember as 'normal'. We fight for our meds sometimes - I have for years asked for several different strengths so I can self-treat the highs and lows if required without returning to a doctor who may take blood samples on a day my TSH is up or down and dose accordingly. We are treated as though we are taking narcotics at times despite the fact that if you are NOT hypothyroid the meds will NOT make your heart race or your metabolism jump as some believe.
Something I have not tried but which many have and it works for them is natural TSH, either in conjunction with the regular medication or alone. And, if synthroid is not working for you to make you feel better in all ways, then a) make sure you are not on a generic - I insist on NO substitutions being on my prescription (I went downhill very quickly for 2 years when Levoxyl, which I take, was not available on the market and I was forced to take a generic, and one year after it has returned with a different manufacturer, I am still not back up to par) and/or b) ask to try another medication (levoxyl is one but there are others - and while all will say they are the same meds, the inactive ingredients can make a BIG difference to some individuals, like me and maybe like you). I also tried the no meds approach - BIG mistake.
What I HAVE found to be helpful for me is avoidance of many foods (many of which I unfortunately like and which are 'good for you' - or at least for those who are not hypothyroid). I don't take iodine supplements but I do try to cook from scratch and always use iodized salt - and not eat out much or buy processed foods. Soy (unfermented) is the biggest of those, but, grapefruit (which is a no-no for many people on meds of many kinds anyway), and all cruciferous/brassica vegetables - especially raw ones and especially things like kale - these are goitrogens - are also on the 'list'. Processed foods which do not contain iodized salt (and most don't) are an issue - so .. those cans of food you like .. umm, not such a great thing.

Read more about what is probably best to avoid or limit here (or on many other sites around the web - this is not radical/pseudo-science)
http://www.thyrophoenix.com/bad_foods.htm